The main qualitative result of the numerical analysis of
Eq. (REF ) performed in [1]}, [2]} is that
the linear stability in the fourth-derivative model is possible,
but the two conditions should be fulfilled.
First of all, the frequency \(k\)  should be essentially smaller than the
Planck mass. The threshold value for \(k\)  slightly depends on the
type of the cosmological solution (dominated by radiation, dust
or cosmological constant), but, in
all cases for \(k < 0.1\,M_P\) , there is no growth of \(h(t,k)\) ,
while such a growth is evident starting from \(k \approx 0.6\,M_P\) .
This requirement exactly corresponds to our expectation that one
needs a Planck density of gravitons to wake up the ghost from the
vacuum. For a small frequency \(k\) , the ghost remains as a virtual
mode and cannot be created from vacuum to become a real particle.
Let us remember that the creation of a ghost from the vacuum
requires positive-energy gravitons with the Planck energy density
(Planck energy in the space volume of a cube of the Planck-scale
Compton wavelength). If the frequency of the gravitational wave is
insufficient, the ghost is not created, and there is no instability.
